Calculate the area of an isosceles triangle with sides 10,10 and 23

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Step-by-Step Solution

Step 1: Identify the sides and draw the altitude

We are given an isosceles triangle with two equal sides of length 10 units and a base of length 23 units. To find the area, we can draw an altitude from the vertex between the equal sides to the base. This altitude will bisect the base.

Step 2: Calculate the length of the bisected base segment

Since the altitude bisects the base, each segment of the base will be half of the total base length.

Step 3: Use the Pythagorean theorem to find the altitude

The altitude, one of the equal sides, and half of the base form a right-angled triangle. We can use the Pythagorean theorem ($a^2 + b^2 = c^2$) to find the height ($h$). However, we find that $h^2$ is negative, which indicates that a triangle with these side lengths cannot exist.